Решить ∫ _{1/2L}^L(1-cospix/2x40)x wrt x

$$\int _ { \frac { 1 } { 2 } L } ^ { L } ( 1 - \cos \frac { \pi x } { 2 x 40 } ) x d x$$

Вычислить

$$\frac{8\pi \sin(\frac{\pi L}{4x_{40}})Lx_{40}-16\pi \sin(\frac{\pi L}{2x_{40}})Lx_{40}+32\cos(\frac{\pi L}{4x_{40}})x_{40}^{2}-32\cos(\frac{\pi L}{2x_{40}})x_{40}^{2}+3\left(\pi L\right)^{2}}{8\pi ^{2}}$$

Дифференцировать по x_40

$$\frac{-\frac{\cos(\frac{\pi L}{4x_{40}})L^{2}}{x_{40}}+\frac{4\cos(\frac{\pi L}{2x_{40}})L^{2}}{x_{40}}+\frac{32\cos(\frac{\pi L}{4x_{40}})x_{40}}{\pi ^{2}}-\frac{32\cos(\frac{\pi L}{2x_{40}})x_{40}}{\pi ^{2}}+\frac{8\sin(\frac{\pi L}{4x_{40}})L}{\pi }-\frac{16\sin(\frac{\pi L}{2x_{40}})L}{\pi }}{4}$$